1 citations · 2 across the 3 of their papers we have counts for
11 papers
Overcoming the curse of dimensionality in the numerical approximation of backward stochastic differential equations
Martin Hutzenthaler, Arnulf Jentzen, Thomas Kruse +1
Backward stochastic differential equations (BSDEs) belong nowadays to the most frequently studied equations in stochastic analysis and computational stochastics. BSDEs in applicati…
Inhomogeneous affine Volterra processes
Julia Ackermann, Thomas Kruse, Ludger Overbeck
We extend recent results on affine Volterra processes to the inhomogeneous case. This includes moment bounds of solutions of Volterra equations driven by a Brownian motion with an…
Multilevel Picard approximations for high-dimensional semilinear second-order PDEs with Lipschitz nonlinearities
Martin Hutzenthaler, Arnulf Jentzen, Thomas Kruse +1
The recently introduced full-history recursive multilevel Picard (MLP) approximation methods have turned out to be quite successful in the numerical approximation of solutions of h…
Nonlinear Monte Carlo methods with polynomial runtime for high-dimensional iterated nested expectations
Christian Beck, Arnulf Jentzen, Thomas Kruse
The approximative calculation of iterated nested expectations is a recurring challenging problem in applications. Nested expectations appear, for example, in the numerical approxim…
Optimal trade execution in an order book model with stochastic liquidity parameters
Julia Ackermann, Thomas Kruse, Mikhail Urusov
We analyze an optimal trade execution problem in a financial market with stochastic liquidity. To this end we set up a limit order book model in which both order book depth and res…
Overcoming the curse of dimensionality in the numerical approximation of Allen-Cahn partial differential equations via truncated full-history recursive multilevel Picard approximations
Christian Beck, Fabian Hornung, Martin Hutzenthaler +2
One of the most challenging problems in applied mathematics is the approximate solution of nonlinear partial differential equations (PDEs) in high dimensions. Standard deterministi…